Question

The accompanying data represent the one-way commuting time on January 15, 2020 of 15 persons who work at a large meat factory. Assuming an approximate normal distribution of commuting time, construct and interpret the 90% confident interval for the mean commuting time.

21.7 26.8 33.1 27.9 23.5 39.0 28.0 24.7 28.4 38.9 30.0 33.6 33.3 34.1 35.1

(Keep in mind the difference between data and stat in TI-84; To compute the summary statistics, use 1-var stat ( ) will do it.) Please inform me which TI-84 app, if you used, helps you to reach the answer.

Answer 1

First, we need to calculate mean and standard deviation

Since we know that

Where n is the number of data points

Now

and n = 15

This implies that

For confidence interval we use t distribution since sample size is less than 30

Confidence interval(in %) = 90

Since we know that

Required confidence interval = (30.54-2.4098, 30.54+2.4098)

Required confidence interval = (28.13, 32.95)

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